Reference : Associative and quasitrivial operations on finite sets: characterizations and enumeration
Scientific congresses, symposiums and conference proceedings : Unpublished conference
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
Computational Sciences
http://hdl.handle.net/10993/36083
Associative and quasitrivial operations on finite sets: characterizations and enumeration
English
Couceiro, Miguel [[LORIA, CNRS - Inria Nancy Grand Est - Université de Lorraine]]
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2-Jul-2018
No
Yes
International
International Symposium on Aggregation and Structures (ISAS 2018)
from 02-07-2018 to 05-07-2018
José Luis García-Lapresta
Miguel Martínez-Panero
David Pérez-Román
Valladolid
Spain
[en] We investigate the class of binary associative and quasitrivial operations on a given finite set. Here the quasitriviality property (also known as conservativeness) means that the operation always outputs one of its input values. We also examine the special situations where the operations are commutative and nondecreasing, in which cases the operations reduce to discrete uninorms (which are discrete fuzzy connectives playing an important role in fuzzy logic).

Interestingly, associative and quasitrivial operations that are nondecreasing are characterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black.

We also address and solve a number of enumeration issues: we count the number of binary associative and quasitrivial operations on a given finite set as well as the number of those operations that are commutative and/or nondecreasing.
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/36083
http://isas2018.uva.es/

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